A nuclear reactor core includes many individual components that have different characteristics that may affect a strategy for efficient operation of the core. For example, a nuclear reactor core has many, e.g., several hundred, individual fuel assemblies (bundles) that have different characteristics and which must be arranged within the reactor core or “loaded” so that the interaction between fuel bundles satisfies all regulatory and reactor design constraints, including governmental and customer specified constraints. Similarly, other controllable elements and factors that affect the reactivity and overall efficiency of a reactor core must also be taken into consideration if one is to design or develop an effective control strategy for optimizing the performance of a reactor core at a particular reactor plant. Such “operational controls” (also referred to interchangeably herein as “independent control-variables” and “design inputs”) include, for example, various physical component configurations and controllable operating conditions that can be individually adjusted or set.
Besides fuel bundle “loading”, other sources of control variables include “core flow” or rate of water flow through the core, the “exposure” and the “reactivity” or interaction between fuel bundles within the core due to differences in bundle enrichment, and the “rod pattern” or distribution and axial position of control blades within the core. As such, each of these operational controls constitutes an independent control-variable or design input that has a measurable effect on the overall performance of the reactor core. Due to the vast number of possible different operational values and combinations of values that these independent control-variables can assume, it is a formidable challenge and a very time consuming task, even using known computer-aided methodologies, to attempt to analyze and optimize all the individual influences on core reactivity and performance.
For example, the number of different fuel bundle configurations possible in the reactor core can be in excess of one hundred factorial. Of the many different loading pattern possibilities, only a small percentage of these configurations will satisfy all of the requisite design constraints for a particular reactor plant. In addition, only a small percentage of the configurations that satisfy all the applicable design constraints are economically feasible.
Moreover, in addition to satisfying various design constraints, since a fuel bundle loading arrangement ultimately affects the core cycle energy (i.e., the amount of energy that the reactor core generates before the core needs to be refueled with new fuel elements), a particular loading arrangement needs to be selected that optimizes the core cycle energy.
In order to furnish and maintain the required energy output, the reactor core is periodically refueled with fresh fuel bundles. The duration between one refueling and the next is commonly referred to as a “fuel-cycle” or “core-cycle” of operation and, depending on the particular reactor plant, is on the order of twelve to twenty-four (typically eighteen) months. At the time of refueling, typically one third of the least reactive fuel are removed from the reactor and the remaining fuel bundles are repositioned before fresh fuel bundles are added. Generally, to improve core cycle energy higher reactivity bundles should be positioned at interior core locations. However, such arrangements are not always possible to achieve while still satisfying plant specific design constraints. Since each fuel bundle can be loaded at a variety of different locations relative to other bundles, identifying a core loading arrangement that produces optimum performance of the core for each fuel-cycle presents a complex and computation-intensive optimization problem that can be very time consuming to solve.
During the course of a core-cycle, the excess energy capability of the core, defined as the excess reactivity or “hot excess”, is controlled in several ways. One technique employs a burnable reactivity inhibitor, e.g., Gadolinia, incorporated into the fresh fuel. The quantity of initial burnable inhibitor is determined by design constraints and performance characteristics typically set by the utility and by the Nuclear Regulatory Commission (NRC). The burnable inhibitor controls most, but not all, of the excess reactivity. Consequently, “control blades” (also referred to herein as “control rods”)—which inhibit reactivity by absorbing nuclear emissions—are also used to control excess reactivity. Typically, a reactor core contains many such control blades which are fit between selected fuel bundles and are axially positionable within the core. These control blades assure safe shut down and provide the primary mechanism for controlling the maximum power peaking factor.
The total number of control blades utilized varies with core size and geometry, and is typically between 50 and 150. The axial position of the control blades (e.g., fully inserted, fully withdrawn, or somewhere in between) is based on the need to control the excess reactivity and to meet other operational constraints, such as the maximum core power peaking factor. For each control blade, there may be, for example, 24 or more possible axial positions and 40 “exposure” (i.e., duration of use) steps. Considering symmetry and other requirements that reduce the number of control blades that are available for application at any given time, there are many millions of possible combinations of control blade positions for even the simplest case. Of these possible configurations, only a small fraction satisfies all applicable design and safety constraints, and of these, only a small fraction is economical. Moreover, the axial positioning of control blades also influences the core cycle energy that any given fuel loading pattern can achieve. Since it is desirable to maximize the core-cycle energy in order to minimize nuclear fuel cycle costs, developing an optimum control blade positioning strategy presents another formidable independent control-variable optimization problem that must also be taken into consideration when attempting to optimize fuel-cycle design and management strategies.
Traditionally, reactor fuel-cycle design and management, including core loading and control blade positioning determinations as well as optimization strategies concerning other variable operational controls, are determined on a “trial-and-error” basis based primarily on the past experiences of the reactor core design engineers. Due to circumstances that require a rapid response to changing plant operating conditions, a core design engineer may be faced with the formidable challenge of specifying values for over 200 independent control-variables within a very short time frame. The impact, for example, of a particular suggested core loading arrangement or a control blade positioning arrangement on reactor performance over the duration of a core-cycle is usually determined by individual computer simulations. If a particular design constraint is not satisfied by an identified arrangement, then the arrangement is modified and another computer simulation is run. Because of the relatively long computer simulation time required for assessing the impact of a change in the value of even a single given independent control-variable, man-weeks of human and computer resources are typically required before an appropriate fuel-cycle design is identified using this procedure.
Moreover, using this trial-and-error approach, once a fuel-cycle design arrangement that satisfies all design and safety constraints has been identified, it may turn out that the identified arrangement may not provide the actual maximum cycle-energy. Therefore, this trial-and-error process must continue until the engineers believe that an optimum fuel-cycle design for the core has been identified. In practice, however, it is very possible that a particular core arrangement that is not consistent with the engineers' past experience may be the actual optimum fuel-cycle design for the core. Such an actual optimum core arrangement, however, may not necessarily be identified through the above described trial and error process.